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Simplifying -9 + 7x2 + x = 7 Reorder the terms: -9 + x + 7x2 = 7 Solving -9 + x + 7x2 = 7 Solving for variable 'x'. Reorder the terms: -9 + -7 + x + 7x2 = 7 + -7 Combine like terms: -9 + -7 = -16 -16 + x + 7x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -16 + x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 0.1428571429x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 0.1428571429x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 0.1428571429x + x2 = 0 + 2.285714286 0.1428571429x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 0.1428571429x + x2 = 2.285714286 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1428571429x + 0.25 + x2 = 2.285714286 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = 2.285714286 + 0.25 Combine like terms: 2.285714286 + 0.25 = 2.535714286 0.25 + 0.1428571429x + x2 = 2.535714286 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.535714286 Calculate the square root of the right side: 1.592392629 Break this problem into two subproblems by setting (x + 0.5) equal to 1.592392629 and -1.592392629.Subproblem 1
x + 0.5 = 1.592392629 Simplifying x + 0.5 = 1.592392629 Reorder the terms: 0.5 + x = 1.592392629 Solving 0.5 + x = 1.592392629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.592392629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.592392629 + -0.5 x = 1.592392629 + -0.5 Combine like terms: 1.592392629 + -0.5 = 1.092392629 x = 1.092392629 Simplifying x = 1.092392629Subproblem 2
x + 0.5 = -1.592392629 Simplifying x + 0.5 = -1.592392629 Reorder the terms: 0.5 + x = -1.592392629 Solving 0.5 + x = -1.592392629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.592392629 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.592392629 + -0.5 x = -1.592392629 + -0.5 Combine like terms: -1.592392629 + -0.5 = -2.092392629 x = -2.092392629 Simplifying x = -2.092392629Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.092392629, -2.092392629}
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